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Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the…
It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying…
We examine the scaling regime for the detrended fluctuation analysis (DFA) - the most popular method used to detect the presence of long memory in data and the fractal structure of time series. First, the scaling range for DFA is studied…
The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the…
Multifractal analysis is a forecasting technique used to study the scaling regularity properties of financial returns, to analyze the long-term memory and predictability of financial markets. In this paper, we propose a novel structural…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…
We investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after the large fluctuations is characterized by…
The performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono- and multifractal models. The reconstruction of the generalized Hurst exponents is used to determine the range of…
We investigate multifractality in the Korean stock-market index KOSPI. The generalized $q$th order height-height correlation function shows multiscaling properties. There are two scaling regimes with a crossover time around $t_c =40$ min.…
Studying the micro-trading behaviors before stock price jumps is an important problem for financial regulations and investment decisions. In this study, we provide a new framework to study pre-jump trading behaviors based on multivariate…
For many externally driven complex systems neither the noisy driving force, nor the internal dynamics are a priori known. Here we focus on systems for which the time dependent activity of a large number of components can be monitored,…
Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high frequency exchange rates of eight major world currencies over 2010-2018 period are used to…
We perform return interval analysis of 1-min {\em{realized volatility}} defined by the sum of absolute high-frequency intraday returns for the Shanghai Stock Exchange Composite Index (SSEC) and 22 constituent stocks of SSEC. The scaling…
The correlation matrix formalism is used to study temporal aspects of the stock market evolution. This formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures. The present…
We study the properties of memory of a financial time series adopting two different methods of analysis, the detrended fluctuation analysis (DFA) and the analysis of the power spectrum (PSA). The methods are applied on three time series:…
We study temporal correlations and multifractal properties of long river discharge records from 41 hydrological stations around the globe. To detect long-term correlations and multifractal behaviour in the presence of trends, we apply…
The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well…
Using a relationship between the moments of the probability distribution of times between the two consecutive trades (intertrade time distribution) and the moments of the distribution of a daily number of trades we show, that the underlying…
Financial markets exhibit an apparent paradox: while directional price movements remain largely unpredictable--consistent with weak-form efficiency--the magnitude of price changes displays systematic structure. Here we demonstrate that…
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses…